Why is $\pi$ so close to $3$? [closed]

pi

$\pi\approx 3.141592654$

Why is it so close to $3$?

I find this intriguing, this cannot be a coincidence.


As you can clearly see from this figure, $2\pi\simeq6\iff\pi\simeq3$, since the side of the inscribed regular polygon is equal to the radius of the circle:

$\qquad\qquad\qquad\qquad$1


Let $a<b$ be integers. Pick a number, which we'll call $\pi'$ in $[a,b]$ uniformly at random. The chance that $\pi'$ is within $\pi-3\approx .1415$ of some integer is $2(\pi-3)\approx .283$.

If something has a near $30\%$ chance of occuring at random, I would say that it could definitely just be a coincidence.

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